{"id":14362,"date":"2018-04-10T22:52:50","date_gmt":"2018-04-10T21:52:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14362"},"modified":"2022-01-11T19:31:03","modified_gmt":"2022-01-11T19:31:03","slug":"a-piscina-que-a-mae-da-marta-comprou-para-colocar-no-jardim","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14362","title":{"rendered":"A piscina que a m\u00e3e da Marta comprou para colocar no jardim"},"content":{"rendered":"<p><ul id='GTTabs_ul_14362' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14362' class='GTTabs_curr'><a  id=\"14362_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14362' ><a  id=\"14362_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14362'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Na Figura 1, est\u00e1 representado um esquema da\u00a0piscina que a m\u00e3e da Marta comprou para colocar no jardim.<br \/>\nA Figura 2 representa um esquema da base da piscina.<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14364\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14364\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png\" data-orig-size=\"811,391\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Piscina\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png\" class=\"aligncenter wp-image-14364\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1-300x145.png\" alt=\"\" width=\"600\" height=\"289\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1-300x145.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1-768x370.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png 811w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><\/p>\n<p>Na Figura 1, [<em>ABCDEFGHIJKL<\/em>] \u00e9 um prisma regular e\u00a0\\(\\overline {BH} = 1,5\\) m.<br \/>\nNa Figura 2, [<em>ABCDEF<\/em>] \u00e9 um hex\u00e1gono,\u00a0\\(\\overline {BC} = 2\\) m e\u00a0\\(\\overline {OM} = \\sqrt 3 \\) m.<\/p>\n<ol>\n<li>Calcula, em litros, a capacidade da piscina.<br \/>\nApresenta os c\u00e1lculos que efetuares.<\/li>\n<li>A m\u00e3e da Marta vai colocar junto da piscina um escorrega como o representado na Figura 3.<br \/>\nA Figura 4 representa um esquema do escorrega da Figura 3.<br \/>\n<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14368\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14368\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png\" data-orig-size=\"875,423\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Escorrega\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png\" class=\"aligncenter wp-image-14368\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a-300x145.png\" alt=\"\" width=\"600\" height=\"290\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a-300x145.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a-768x371.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png 875w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><br \/>\nQual \u00e9, em graus, a amplitude do \u00e2ngulo \u03b1?<br \/>\nApresenta os c\u00e1lculos que efetuares e, na tua resposta, escreve o resultado arredondado \u00e0s unidades.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14362' onClick='GTTabs_show(1,14362)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14362'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Na Figura 1, est\u00e1 representado um esquema da piscina que a m\u00e3e da Marta comprou para colocar no jardim.<br \/>\nA Figura 2 representa um esquema da base da piscina.<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14364\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14364\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png\" data-orig-size=\"811,391\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Piscina\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png\" class=\"aligncenter wp-image-14364\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1-300x145.png\" alt=\"\" width=\"600\" height=\"289\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1-300x145.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1-768x370.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1.png 811w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><\/p>\n<p>Na Figura 1, [<em>ABCDEFGHIJKL<\/em>] \u00e9 um prisma regular e \\(\\overline {BH} = 1,5\\) m.<br \/>\nNa Figura 2, [<em>ABCDEF<\/em>] \u00e9 um hex\u00e1gono, \\(\\overline {BC} = 2\\) m e \\(\\overline {OM} = \\sqrt 3 \\) m.<\/p>\n<\/blockquote>\n<ol>\n<li>O volume da piscina, em metros c\u00fabicos, \u00e9:<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{Piscina}}}&amp; = &amp;{6 \\times \\frac{{\\overline {BC} \\times \\overline {OM} }}{2} \\times \\overline {BH} }\\\\{}&amp; = &amp;{6 \\times \\frac{{2 \\times \\sqrt 3 }}{2} \\times 1,5}\\\\{}&amp; = &amp;{9\\sqrt 3 }\\\\{}&amp; \\approx &amp;{15,588}\\end{array}\\]<br \/>\nPortanto, a piscina tem, aproximadamente, 15588 litros de capacidade.<br \/>\n\u00ad<\/li>\n<li>No tri\u00e2ngulo ret\u00e2ngulo da Figura 4, vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} \\alpha = \\frac{{1,8}}{2}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} \\alpha = 0,9}\\\\{}&amp; \\Leftrightarrow &amp;{\\alpha = {{{\\mathop{\\rm tg}\\nolimits} }^{ &#8211; 1}}\\left( {0,9} \\right)}\\\\{}&amp;{}&amp;{\\alpha \\approx 42^\\circ }\\end{array}\\]<br \/>\nPortanto, \\(\\alpha \\approx 42^\\circ \\).<br \/>\n<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14368\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14368\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png\" data-orig-size=\"875,423\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Escorrega\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png\" class=\"aligncenter wp-image-14368\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a-300x145.png\" alt=\"\" width=\"600\" height=\"290\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a-300x145.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a-768x371.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1a.png 875w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14362' onClick='GTTabs_show(0,14362)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na Figura 1, est\u00e1 representado um esquema da\u00a0piscina que a m\u00e3e da Marta comprou para colocar no jardim. A Figura 2 representa um esquema da base da piscina. Na Figura 1,&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14363,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,493,490,492,109],"series":[],"class_list":["post-14362","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-9-o-ano","tag-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente","tag-volume"],"views":3033,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag72-1b.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14362","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14362"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14362\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14363"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14362"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}